Calculating the Value of a Mathematical Expression

Let's break down the given mathematical expression step by step to find its value. The expression is: ${\(\frac{3}{4}\) of 60 ÷ 9} × 0.02$.

To solve this, we need to follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS. This order tells us which operation to perform first:

• B/P: Brackets/Parentheses
• O/E: Order/Exponents
• D/M: Division/Multiplication (from left to right)
• A/S: Addition/Subtraction (from left to right)

In our expression, we have 'of' (which means multiplication), division, and multiplication. The part inside the curly braces ${\(\frac{3}{4}\) of 60 ÷ 9}$ should be calculated first.

Step-by-Step Calculation of the Expression

Step 1: Calculate '{\(\frac{3}{4}\) of 60}'

The term 'of' means multiplication. So, we calculate ${\frac{3}{4} \times 60}$.

${\frac{3}{4} \times 60 = \frac{3 \times 60}{4} = \frac{180}{4} = 45}$

So, ${\frac{3}{4} \text{ of } 60}$ equals 45.

Step 2: Perform the Division within the Braces

Now, we take the result from Step 1 (45) and divide it by 9, as indicated within the braces.

${45 \div 9 = \frac{45}{9} = 5}$

The value of ${\(\frac{3}{4}\) of 60 ÷ 9}$ is 5.

Step 3: Perform the Final Multiplication

Finally, we take the result from Step 2 (5) and multiply it by 0.02.

${5 \times 0.02}$

To multiply a whole number by a decimal, you can multiply the numbers as if they were whole numbers and then place the decimal point in the result. ${5 \times 2 = 10}$. Since 0.02 has two decimal places, the result must also have two decimal places. Starting from the right, we move the decimal point two places to the left.

${5 \times 0.02 = 0.10}$

The value of the expression ${\(\frac{3}{4}\) of 60 ÷ 9} × 0.02$ is 0.10.

Revision Table: Order of Operations (BODMAS/PEMDAS)

Additional Information: Decimal Multiplication

Multiplying decimals is a common operation in mathematics. Here's a quick reminder:

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in the numbers you multiplied.
3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in the previous step.

Example: To calculate ${5 \times 0.02}$:

• Multiply 5 by 2 (ignoring decimals): ${5 \times 2 = 10}$.
• Count decimal places: 5 has 0, 0.02 has 2. Total is ${0 + 2 = 2}$ decimal places.
• Place decimal in 10: Start from the right and move 2 places left. ${1.0 \rightarrow 0.10}$.

The result is 0.10.